Page:Elementary Principles in Statistical Mechanics (1902).djvu/127

Rh Moreover, if we eliminate $$d\psi$$ from (326) by the equation obtained by differentiating (325), we get  or by (321),  Except for the signs of average, the second member of this equation is the same as that of the identity  For the more precise comparison of these equations, we may suppose that the energy in the last equation is some definite and fairly representative energy in the ensemble. For this purpose we might choose the average energy. It will perhaps be more convenient to choose the most common energy, which we shall denote by $$\epsilon_0$$. The same suffix will be applied to functions of the energy determined for this value. Our identity then becomes It has been shown that  when $$n > 2$$. Moreover, since the external coördinates have constant values throughout the ensemble, the values of $$d\phi/da_1$$, $$d\phi/da_2$$, etc. vary in the ensemble only on account of the variations of the energy ($$\epsilon$$), which, as we have seen, may be regarded as sensibly constant throughout the ensemble, when $$n$$ is very great. In this case, therefore, we may regard the average values